Temat: CR manifolds - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Special normal form of a hyperbolic CR-manifold in ℂ⁴
Autorzy:: Ežov, Vladimir
Schmalz, Gerd
Powiązania:: https://bibliotekanauki.pl/articles/1294219.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: CR-manifolds
invariants
classification
Opis:: We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate change.
Źródło:: Annales Polonici Mathematici; 1998, 70, 1; 99-107
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Non-solvability of the tangential ∂̅-system in manifolds with constant Levi rank
Autorzy:: Zampieri, Giuseppe
Powiązania:: https://bibliotekanauki.pl/articles/1207981.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: CR manifolds
∂̅ and $∂̅^b$ problems
tangential CR complex
Opis:: Let M be a real-analytic submanifold of $ℂ^n$ whose "microlocal" Levi form has constant rank $s^{+}_{M} + s^{-}_{M}$ in a neighborhood of a prescribed conormal. Then local non-solvability of the tangential ∂̅-system is proved for forms of degrees $s^{-}_{M}$, $s^{+}_{M}$ (and 0).
This phenomenon is known in the literature as "absence of the Poincaré Lemma" and was already proved in case the Levi form is non-degenerate (i.e. $s^{-}_{M} + s^{+}_{M} = n - codim M$). We owe its proof to [2] and [1] in the case of a hypersurface and of a higher-codimensional submanifold respectively. The idea of our proof, which relies on the microlocal theory of sheaves of [3], is new.
Źródło:: Annales Polonici Mathematici; 2000, 74, 1; 291-296
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On the local meromorphic extension of CR meromorphic mappings
Autorzy:: Merker, Joël
Porten, Egmont
Powiązania:: https://bibliotekanauki.pl/articles/1294226.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: CR generic currents
scarred CR manifolds
removable singularities for CR functions
deformations of analytic discs
CR meromorphic mappings
Opis:: Let M be a generic CR submanifold in $ℂ^{m+n}$, m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple $(f,_f,[Γ_f])$, where: 1) $f: _f → Y$ is a ¹-smooth mapping defined over a dense open subset $_f$ of M with values in a projective manifold Y; 2) the closure $Γ_f$ of its graph in $ℂ^{m+n} × Y$ defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) $d[Γ_f] = 0$ in the sense of currents. We prove that $(f,_f,[Γ_f])$ extends meromorphically to a wedge attached to M if M is everywhere minimal and $^ω$ (real-analytic) or if M is a $^{2,α}$ globally minimal hypersurface.
Źródło:: Annales Polonici Mathematici; 1998, 70, 1; 163-193
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: On normal CR-submanifolds of S-manifolds
Autorzy:: Cabrerizo, José
Fernández, Luis
Fernández, Manuel
Powiązania:: https://bibliotekanauki.pl/articles/967514.pdf
Data publikacji:: 1993
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: S-manifolds
normal CR-submanifolds
S-space forms
Opis:: Many authors have studied the geometry of submanifolds of Kaehlerian and Sasakian manifolds. On the other hand, David E. Blair has initiated the study of S-manifolds, which reduce, in particular cases, to Sasakian manifolds ([1, 2]). I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds of S-manifolds. The purpose of the present paper is to study a special kind of such submanifolds, namely the normal CR-submanifolds. In Sections 1 and 2, we review basic formulas and definitions for submanifolds in Riemannian manifolds and in S-manifolds, respectively, which we shall use later. In Section 3, we introduce normal CR-submanifolds of S-manifolds and we study some properties of their geometry. Finally, in Section 4, we consider those submanifolds in the case of the ambient S-manifold being an S-space form.
Źródło:: Colloquium Mathematicum; 1993, 64, 2; 203-214
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

Artykuł

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